Yes. If you can access the net fine on the other machines then all the info needed is there and you don't need to input anything.
If you do have problems, just make sure your new machine is set to automatically detect settings / direct connection to the internet, and that it is not set to dial a location, (or whatever it's called in Internet Explorer's / firefox connections page) and you should be good to go.
The only things you will have to enter are the server settings for your E-mail into your E-mail program's account settings.
These can be found here:
http://www.virgin.net/helpme/email/questions/1.html
Slightly different ones if you are on the old NTL servers.
I think it is pop.ntlworld.com and smtp.ntlworld.com and then you'l be prompted for your password.